The ultracentrifuge is an important tool for separating and analyzing proteins in biological research. Because of the enormous centripetal accelerations that can be achieved, the apparatus must be carefully balanced so that each sample is matched by another on the opposite side of the rotor shaft. Failure to do so is a costly mistake. Any difference in mass of the opposing samples will cause a net force in the horizontal plane on the shaft of the rotor. Suppose that a scientist makes a slight error in sample preparation, and one sample has a mass 9.0 mg greater than the opposing sample. If the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples?

Researchers conducted an experiment to identify the effects of three different hand sanitizers on the growth of bacteria. the researchers grew one type of bacteria in twenty-four identical covered petri dishes. then, they opened eighteen petri dishes and applied the three hand sanitizers to six petri dishes each. they left the remaining six petri dishes closed as a control group. when the researchers measured the growth of bacteria two days later, the six dishes that had no hand sanitizer showed the least amount of bacterial growth. the researchers concluded that not using any hand sanitizer would lead to the least bacterial growth. which statement best explains why the researchers’ conclusion was not justified? the experiment tested too many variables. the control group was not treated the same as the experimental group. the sample size of twenty-four petri dishes is not large enough. the single type of bacteria is not adequate to make any conclusions.